About Banker's Discount
A banker does not wait for a bill to mature. The banker pays the holder today and collects the full amount later, so the charge made is simply interest on the amount of the bill for the time still to run. That charge is the banker discount, and it is always larger than the true discount on the same bill.
What you need to understand
- The banker discount is the simple interest on the amount of the bill for the unexpired time.
- A banker discount is calculated on the amount, while the true discount is calculated on the present worth.
- Because the amount is larger than the present worth, the banker discount always exceeds the true discount.
- The excess of the banker discount over the true discount is the interest on the true discount.
- Banker gain is another name for that excess, since it is what the banker makes by charging interest on the larger figure.
- Given any two of the three quantities, amount, discount and rate multiplied by time, the third follows immediately.
Formulas to remember
How to work through these questions
- Decide which discount the question is about, because the two differ and the wording is the only clue.
- Work out rate multiplied by time as a single number before substituting.
- When the discount is given and the amount is wanted, multiply the discount by 100 and divide by rate multiplied by time.
- When the true discount is given, first find the present worth and add it to the true discount to get the amount.
- Check that the banker discount comes out larger than the true discount, which is always the case.
Mistakes that cost marks
- Giving the true discount when the banker discount was asked for, which understates the answer.
- Calculating the banker discount on the present worth instead of on the amount.
- Multiplying where the formula calls for dividing when working back to the amount.
- Adding the discount to the amount instead of subtracting it to find the present worth.
- Mixing the two discounts up in the middle of a calculation and reporting the wrong base.
Worked example
The banker discount on a bill due 1 year hence at 10% per annum is Rs. 30. Find the amount of the bill.
- The banker discount is simple interest on the amount due.
- So amount x 10 x 1 / 100 = 30.
- Rearranging, the amount is 30 x 100 / 10 = 300.
- Check: 10% of 300 for one year is 30, which matches the discount given.
Answer: Rs. 300
Practice questions with answers
A few Banker's Discount questions with the full solution shown, so you can see
how the method is applied before you attempt the timed set.
Question 1
Find the banker's discount on Rs. 2400 due 2 years at 25% per annum.
-
A
1200
-
B
800
-
C
2400
-
D
1600
Answer: Option A — with explanation
The banker's discount is simply the simple interest on the amount due for the unexpired time.
= 2400 x 25 x 2 / 100 = 1200.
The true discount is the interest on the present worth rather than on the amount, so it is always the smaller of the two.
Common mistakes
- repeated the amount due: 2400
- gave the true discount instead of the banker's discount: 800
- gave the present worth instead of a discount: 1600
Question 2
The banker's discount on a bill due 3 years at 20% per annum is Rs. 1440. Find the amount of the bill.
-
A
1440
-
B
2400
-
C
864
-
D
3840
Answer: Option B — with explanation
The banker's discount is simple interest on the amount due.
So amount x 20 x 3 / 100 = 1440, giving amount = 1440 x 100 / 60 = 2400.
Common mistakes
- multiplied where the formula calls for dividing: 864
- gave the discount instead of the amount of the bill: 1440
- added the discount on top of the amount: 3840
Question 3
If the true discount on a bill payable 4 years at 5% is Rs. 80, find the banker's discount on the same bill.
Answer: Option D — with explanation
The true discount is the interest on the present worth, so present worth = 80 x 100 / 20 = 400.
The amount due is 400 + 80 = 480.
The banker's discount is the interest on that amount: 480 x 20/100 = 96.
Common mistakes
- applied the rate and time to the discount itself: 16
- doubled the true discount: 160
- repeated the true discount: 80
Question 4
Find the banker's discount on Rs. 2600 due 3 years at 10% per annum.
-
A
600
-
B
780
-
C
2000
-
D
2600
Answer: Option B — with explanation
The banker's discount is simply the simple interest on the amount due for the unexpired time.
= 2600 x 10 x 3 / 100 = 780.
The true discount is the interest on the present worth rather than on the amount, so it is always the smaller of the two.
Common mistakes
- gave the present worth instead of a discount: 2000
- repeated the amount due: 2600
- gave the true discount instead of the banker's discount: 600
Question 5
The banker's discount on a bill due 4 years at 15% per annum is Rs. 1320. Find the amount of the bill.
-
A
792
-
B
3520
-
C
1320
-
D
2200
Answer: Option D — with explanation
The banker's discount is simple interest on the amount due.
So amount x 15 x 4 / 100 = 1320, giving amount = 1320 x 100 / 60 = 2200.
Common mistakes
- gave the discount instead of the amount of the bill: 1320
- added the discount on top of the amount: 3520
- multiplied where the formula calls for dividing: 792
Frequently asked questions
What is the difference between the banker discount and the true discount?
The banker discount is interest on the amount of the bill. The true discount is interest on the present worth, which is smaller. So the banker discount is the larger of the two.
What is banker gain?
It is the excess of the banker discount over the true discount. It represents the extra the banker earns by charging interest on the amount rather than on the present worth.
How do I find the amount if the banker discount is given?
Multiply the discount by 100 and divide by rate multiplied by time. A discount of Rs. 30 at 10 per cent for one year corresponds to an amount of Rs. 300.
Can the banker discount ever be smaller than the true discount?
No. The amount is always greater than the present worth, so interest on the amount is always the greater figure.
